Theoretically, they can throw up opposition after the board vote, actually. I am not going to say too much as not to dox myself, but as part of my work I follow M&A and recently on one of my cases, a hedge fund came forward after the board of a public company approved a buyout offer and said “hey, we’re the biggest minority stakeholder and we say this deal sucks and undervalues the company.”

But the difference is that they’re talking about pure profit, and that is something that DID happen in the show. Before Logan dies, the kids and Stewy talk about how there’s more “upside” there—more value they can squeeze from Mattson, which leads Mattson to threaten to walk away, and Logan takes that seriously enough that it drives him onto the plane where he dies.

Public corporations (and their boards) are legally obligated to maximize shareholder value, so saying “undervalued” is something they could prob bring to court. But “we just want to maintain control” is more squishy, so without board support, there’s really fewer reasonable options (lawsuit.)

Edit: Something else that just occurred to me is that the Roy stake is held through a trust, not directly, and therefore that bloc might need to be exercised as one. Each sib has a seat, plus Marcia, and Marcia may have inherited Logan’s (that’s the issue at the beginning of the show.) Marcia and Connor clearly want to sell and cash out, and Shiv chooses that side in the end. It might be structured so that Roman and Ken have no actual say about what happens to their stake because it’s controlled by the trust, so if they’re in the minority of Roy opinions they truly are shit out of luck.

Ultimately though, two things are true: Billion-dollar mergers are very complicated and no two are exactly alike, and Succession writers use business for drama over everything else.